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Research Article
Shee-Ping Chen
Buddhist Tzu Chi Stem Cells Centre
Corresponding Author
ORCiD: https://orcid.org/0000-0001-6357-8369
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Georg Cantor defined countable and uncountable sets for infinite sets. Natural number set is defined as a countable set, and real number set is proven as an uncountable set by Cantor’s diagonal method. However, in this paper, natural number set will be proven as an uncountable set using Cantor’s diagonal method, and real number set will be proven as a countable set by Cantor’s definition. The process of argumentation provides us new perspectives to consider about the size of infinite sets.
Keywords
Cantor’s diagonal method, countable, uncountable, infinite sets, set theory
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A new preprint design is coming!
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This is a preprint, a preliminary version of a manuscript that has not completed peer review at a journal. Research Square does not conduct peer review prior to posting preprints. The posting of a preprint on this server should not be interpreted as an endorsement of its validity or suitability for dissemination as established information or for guiding clinical practice.
Research Article
Shee-Ping Chen
Buddhist Tzu Chi Stem Cells Centre
Corresponding Author
ORCiD: https://orcid.org/0000-0001-6357-8369
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
History
CURRENT STATUS: Posted
The most recent version of this article is available here.
No community comments so far
Version 1
Posted 30 Mar, 2021
No comments provided
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Pure Mathematics
License:
This work is licensed under a CC BY 4.0 License. Read Full License
Declarations:
Declarations
- The author has confirmed that a statement listing potential conflicts of interest or lack thereof is included in the text.
The most recent version of this article is available here.
Georg Cantor defined countable and uncountable sets for infinite sets. Natural number set is defined as a countable set, and real number set is proven as an uncountable set by Cantor’s diagonal method. However, in this paper, natural number set will be proven as an uncountable set using Cantor’s diagonal method, and real number set will be proven as a countable set by Cantor’s definition. The process of argumentation provides us new perspectives to consider about the size of infinite sets.
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